Acoustic well logging techniques and tools are extensively described in the art. Acoustic well logging is used to provide surveys of formations traversed by earth boreholes. In particular, measurements are made of the velocities of acoustic waves to reveal valuable information concerning the type of rocks and the porosity of the rocks in the formations surrounding the borehole. A commonly measured acoustic parameter is the slowness of compressional waves measured in micro-seconds per foot. However, it is desirable that other acoustic wave parameters such as the slowness of shear waves be determined.
Identifying the compressional wave and measuring its slowness is generally not difficult. It is the fastest propagating wave in the formation, is non-dispersive, and is the first to reach an array of borehole receivers, when a short burst of energy from a nearby transmitter propagates through the formation.
Measuring shear slowness is considerable more difficult. Because it propagates more slowly, the shear wave arrives after the compressional wave. Therefore, its arrival is typically obscured by compressional energy and slowness determination directly from arrival time is at best difficult and at times impossible.
The areas where shear wave slowness data theoretically or emperically can be applied are diverse. Some of the application areas are seismic amplitude calibration and interpretation, sand control, formation fracturing, reservoir material balance and subsidence studies, lithology, porosity and geopressure prediction.
While rich in possible application areas, shear slowness is difficult to measure automatically with conventional acoustical devices and detection procedures. Except in limited lithology-logging conditions, manual examination of wave forms commonly is required to extract shear slowness. Even then, there has been considerable uncertainty in shear arrivals on short-space tools, due to compressional wave interferrence. In softer rocks, conventional tools simply do not transmit distinct shear arrivals.
Current axially arranged transmitter-receiver tools are designed primarily for detection of compressional waves. Down hole amplifiers adjusted to accentuate the first compressional wave arrival normally saturate through the shear and the late compressional regions of the wave form. When down hole gain is reduced to eliminate amplifier saturation, one observes that initial shear arrivals generally are super-imposed on the later portions of the compressional arrivals with contributions from normal modes arrivals also known as reflected modes other than Stoneley. These contributions make the signal analysis for the direct determination of shear and normal modes slowness impractical at the present state of the art. The problem is compounded in that the initial shear energy commonly is on the same order of magnitude as the normal modes wave energy. Additionally the normal modes wave onset, is almost always obscured by shear wave interference. In some lithologies, such as slow shale when the shear velocity is on the same order of magnitude, or less, than the sound velocity in the fluid then a direct shear arrival is no longer observed by the conventional sonic logging tools. In the zero frequency limit the shear modulus may be determined from the phase velocity of the Stoneley wave if the borehole fluid velocity and fluid density are known. In the higher frequency domains the shear modulus can be determined from the phase velocity of either the Stoneley or the normal modes arrivals when additional parameters are available.
Techniques have been developed for determining normal mode arrivals slowness where the normal modes arrivals are at least partially obscured by the presence of the shear wave. One such technique is described in Co-pending Application filed by Co-employees, Thomas W. Parks and Charles F. Morris entitled "Method and Apparatus for Determining Accoustic Wave Parameters from Acoustic Well Logging Wave Forms" as described in application Ser. No. 372,271, now U.S. Pat. No. 4,562,557, filed Apr. 27, 1982, and assigned to the same assignee as the present application.
In the Parks, et al application, a method is described for estimating or determining the slowness of various wave components of signals received from a linear array of sonic well logging receivers. One of the wave components is the first reflected mode component. The method of determining or estimating parameters of these composite acoustic waves arriving sequentially to the plurality of points spaced vertically along the length of a borehole generally comprises the steps of generating acoustic energy in the borehole and receiving that energy at each of the points after refraction, reflection and direct transmission through and along the formation adjacent to the borehole. A window is established, having a predetermined length and moveout. This window is positioned along the composite wave and the energy received is multiplied at each point by the window, which is delayed by an amount proportional to the transmitter-spacing, thereby attenuating interferring waves. A Fourier transform is generated of that portion of the received energy multiplied by the window to produce a plurality of complex signals in the frequencey domain, which are simultaneously analyzed to obtain an estimate of the parameters. A different moveout is then established for the window and for each different moveout position, the Fourier transform is produced and analyzed. The window is then incremented along the composite waves and the above steps of multiplying, transformation and analysis are performed to obtain the best estimate of the parameters.
The foregoing technique operates well where the composite waves indeed include the shear wave. There are, however, formation conditions that severely attenuate the propogation of the shear wave or instances where the shear wave will not be detected. A need therefore, has remained for an accurate, versatile and reliable method and apparatus for estimating shear wave velocities under all logging conditions, including those where the shear wave is highly attenuated or not detectable.
The phenomenon of normal modes propagating in a fluid-filled borehole has received considerable attention in literature. At long distances from the transmitter, most of the energy in the sonic wave form is contained in the modes. This factor alone would justify studies of their properties. In addition, it has been proposed to use estimates of modal amplitude, phase slowness and attenuation to infer, indirectly, formation parameters of interest, including shear slowness and attenuation. One such proposal study is described in U.S. Pat. No. 4,131,875 issued on Dec. 26, 1978 entitled "Method and Apparatus for Acoustic Logging of a Borehole" and assigned to the assignee of the present application by J. D. Ingram. The patent discloses a method and apparatus where under conditions of soft formations, the amplitude of the Stoneley waves are used to determine both the formation shear velocity and attenuation.
The Stoneley mode is routinely observed in field data, but there has yet to be a convincing demonstration in the literature of it being used to make a log. For example, Cheng and Toksoz in their paper entitled "Elastic Wave Propogation in a Fluid-Filled Borehole and Synthetic Acoustic Logs" appearing in Geophysics, Volume 46, No. 7, pages 1042-1053 of July 19, 1981, claimed to identify trapped modes in field data recorded by a commercial tool. Their evidence consists only of visual comparisons between field wave forms and synthetic wave forms. This is an inclusive procedure, first because of the complicated dependence of the modes on the physical parameters of the borehole, and second, because the trapped modes are highly dispersive, so they have no simple time-space dependence.
Methods and apparatus have been proposed for the indirect determination of the shear modulus by measuring the phase velocity of a guided wave of accoustic energy, for example, the Stoneley wave, and utilizing it to estimate the shear modulus and the shear slowness. This technique is described in Co-pending application Ser. No. 434,658, filed Oct. 15, 1982 now U.S. Pat. No. 4,575,830, by Josephine Murray and John Ingram, for "Indirect Shear Wave Determination." This applicaton is assigned to the same assignee as the present application. The method of the Co-pending application utilizes at least four full waveform receiver signals and a "window," which is placed over the Stoneley arrival of each waveform. The Fourier transform of each windowed portion of the waveform is produced and from the Fourier transform, the phase velocity of the Stoneley wave is determined and the shear modulus estimated. From the relative shear modulus, the density of the mud, the density of the formation and an estimated value of compressional velocity of acoustic energy through the borehole mud is determined the shear velocity or slowness of the formation. More particularly, that method involves the detection of acoustic waves arriving sequentially at a plurality of points spaced vertically along the length of the borehole from a transmitter and windowing the acoustic waves with a window of predetermined length and moveout which is positioned along the received waves relative to the estimated arrival of the Stoneley wave. The signal is multiplied by the window and a Fourier transform of the multiplied signal is taken to produce a plurality of complex signals in the frequency domain. The cross-spectral magnitude and phase is determined for each of the adjacent pairs of receiver signals and the phase velocity is computed from the phase at each frequency. The cross-spectral magnitudes are scanned for a peak in the selected frequency range to identify the frequency at which the peak occurs. From the phase velocity versus frequency relationship, a value of guided wave phase velocity is selected at the identified frequency and an estimate is made of the ratio of the Lame constants. The Lame constants, an estimate of formation density and mud density, together with an estimate of the velocity of acoustic energy in the mud, are utilized to estimate the value of shear wave velocity or slowness.